# Questions tagged [young-tableaux]

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### Expansion of polytabloids in the standard basis

would like to know the most efficient way to write a polytabloid in terms of standard ones. I know the Garnir elements, but using them to do calculations is hard. I also read about "quadratic ...
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### RSK correspondence

Up to now, what are the difference ways we know to define RSK correspondence? I already know: By insertion and recording tableau. Ball construction or Viennot's geometric construction. Growth diagram ...
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### Plane partitions with equal margins

A plane partition of $n$ is an table of integers $A=(a_{ij})$ which add up to $n$ and non-increase in rows and columns. For example, $$A= \begin{matrix} 331 \\ 32 \ \ \\ 11 \ \ \end{matrix}$$ is a ...
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### Tableaux switching

I'm reading the article Tableau Switching: Algorithms and Applications by Benkart, Sottile, and Stroomer. Do you know if there are any articles or books that talk more about the properties of tableau ...
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### Determinantal formula for plane partitions of shifted shape

For $\lambda = (\lambda_1,\ldots,\lambda_{\ell})$ a partition, a (weak) plane partition of shape $\lambda$ is a filling of the Young diagram of $\lambda$ with nonnegative integers such that entries ...
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### Tensoring irreducible $B$-series representations/ Type B Littlewood-Richardson

When tensoring finite dimensional representations of the Lie algebra ${\frak sl}_n$, we have an explicit algorithm given in terms of Young diagrams. See Section 4 of this paper. Do there exist ...
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### Restricted Cauchy identity

Is there some reference for sums like: $$\sum_{\nu \subset \mathrm{[1,n] x[1, m]}}s_{\nu}(x)s_{\nu}(y)t^{|\nu|}$$ $$\sum_{\nu \subset \mathrm{[1,n] x[1, m]}}s_{\nu}(x)s_{\nu}(y)\cdot|\nu|$$ (summation ...
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### Constructing a centrally primitive idempotent in the group algebra of the symmetric group

Consider the group algebra of the symmetric group $\mathbb{C} S_k$. Given some Young tableau $T$ of shape $\lambda$, let $a_{\lambda,T}$ and $b_{\lambda,T}$ be the row symmetrizer and column ...
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### Continuous analogues of Schützenberger promotion

Has anyone studied continuous analogues of Schützenberger promotion, and in particular, a flow on (a suitable subset of) the order polytope of a poset? Here’s what I have in mind: Given a poset $P$, ...
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### Major index generating polynomial for border-strip tableaux

The Question in its original form has been answered, but there is a follow-up, see the end of the post. A border-strip is a skew Young diagram that does not contain a $2 \times 2$-box. A border-strip ...
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### Identities satisfied by the image of the Young symmetrizer

Consider a partition $\lambda=(r_1,\ldots,r_k)$ of an integer $n$ and the corresponding Young diagram with rows of length $r_1,\ldots,r_k$ (hence ordered in non-increasing order). Counting the column ...
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### Counting the orbits of a set of tabloids under the action of a Young subgroup

Let $\lambda = (\lambda_1 \geq \lambda_2 \geq \cdots \geq \lambda_k)$ and $\mu = (\mu_1 \geq \mu_2 \geq \cdots \geq \mu_\ell)$ be partitions of a positive integer $n$. As in Fulton's book on Young ...
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### On an asymptotic formula of Keating and Snaith involving the Riemann zeta function

Keating and Snaith have a famous conjecture on the asymptotics of the integral $\int_0^T |\zeta(\frac 12+it)|^{2k}\, dt$, where $\zeta$ denotes the Riemann zeta function. See page 510 of the book ...
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### Does flipping Young diagrams has anything to do with Fourier?

Here's a chaser to this question. Recall the proof that the number of partition of an integer $n$ into at most $k$ addends is the same as the number of partition of an integer $n$ into integers no ...
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Consider a Young diagram $\lambda = (\lambda_1,\ldots,\lambda_\ell)$. For a square $(i,j) \in \lambda$, define hook numbers $h_{ij} = \lambda_i + \lambda_j' -i - j +1$ and complementary hook numbers $... 0answers 190 views ### Characterizing the RSK corespondance The Robinson-Schensted-Knuth correspondence is an algorithm which takes as input a word$w$on the alphabet$\{1,\dots,n\}$of length$k$and returns a pair of a tableau$P(w)$and a standard tableau$...
Let's consider the Littlewood-Richardson coefficients $c^{\lambda}_{\mu \nu}$ so that \begin{equation} V_\mu \otimes V_\nu = \bigoplus_\lambda V_\lambda^{\oplus c^{\lambda}_{\mu \nu}} \end{equation} ...